FERROMAGNETIC RELAXATION IN POROUS POLYCRYSTALLINE FERRITES

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FERROMAGNETIC RELAXATION IN POROUS POLYCRYSTALLINE FERRITES

Q. Vrehen, A. Broese, van Groenou

To cite this version:

Q. Vrehen, A. Broese, van Groenou. FERROMAGNETIC RELAXATION IN POROUS POLY- CRYSTALLINE FERRITES. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-156-C1-158.

�10.1051/jphyscol:1971151�. �jpa-00214478�

JOURNAL DE

Codloque C 1, supplkment au no 2-3, Tome 32, Rvrier-Mars 1971, page C 1 - 156

FERROMAGNETIC RELAXATION IN POROUS POLYCRYSTALLINE FERRITES

by

Q. H. F. VREHEN and A. BROESE van GROENOU

Philips Research Laboratories N. V. Philips' Gloeilampenfabrieken, Eindhoven-Netherlands

Rbum6.

On a mesure la largeur de raie effective W d'echantillon de YIG polycristallin de porositk comprise entre 0,006 et 0,04. Les mesures ont kt6 effectukes a la frequence de 9 GHz pour des champs appliques He compris entre 1,s et 8 kOe. Les valeurs de W en dehors du domaine d'existence des ondes de spin sont plus Blevkes que le prkvoit la thkorie. Une modification de la thkorie est proposk pour tenir compte de la perturbation des ondes de spin elles-m6mes par la porosite. L'accord entre la theorie et l'expkrience est bon.

Abstract. - The effective linewidth W has been measured in polycrystalline YIG with porosities between 0.006 and 0.04, at a frequency of 9 GHz and for external magnetic fields He between 1.5 kOe and 8 kOe. The values of W outside the spinwave manifold are much larger than predicted by existing spin wave theories. A new treatment is proposed, in which secondary scattering of the spin waves is taken into account, by considering the spin waves to be broadened over a field range of 4 nM. Fair agreement is obtained between theory and experiment.

I. Introduction.

The measurement of the effec- tive linewidth W, as described by Vrehen [I], allows the study of ferromagnetic relaxation both inside and outside the spin wave (SW) manifold. Experi- mental data (see section 11) on porous ferrites show that porosity induced relaxation exists over a wide range of fields above and below the manifold. This field range is of the order of 4 nM (M saturation magnetization). The original SW theory by Sparks et al. [2] predicts relaxation only within the mani- fold. According to a modified theory by Motizuki et al. [3] losses can extend over a field range of the order of p.4 nM on both sides of the manifold (p is the porosity), as a result of secondary scattering, i. e., the perturbation of the manifold itself by the porosity. In section I11 we explain why the effects of secondary scattering are more serious than assu- med by Motizuki et al. [3], and we propose a modi- fication of the theory which describes our experi- ments fairly well.

11. Experimental results. - We measured W = 2 M Im ( 1 / ~ + )

sented for polycrystalline YIG with p = 0.006, 0.015 and 0.04. For He > 5 kOe, W has a constant intrinsic value of 3 Oe. For 2.4 kOe < He < 5 kOe one observes additional relaxation, a small part of which results from anisotropy broadening and the remainder from porosity broadening. The contribu- tion from anisotropy broadening can be calculated on the basis of recent work by Schlomann 141, Pat- ton [5] and the present authors [6, 71 ; it explains in particular the peak near 3 100 Oe in the curve for p = 0.006. The porosity induced part of W extends from 2.4 kOe up to nearly 5 kOe for all values of p, and it is proportional to p for all values of He. Note that the SW manifold extends from 3 kOe up to 3.8 kOe.

111. Theoretical considerations and discussion. - 111. I THE SPIN WAVE MODEL. - We consider the model of a spherical cavity at the center of a sphe- rical sample, and we assume M and He to be parallel to the z-axis. Hi is the internal field that would be present without the pore. Sparks et al. [2] obtained the following expression for W in this model :

I r 1

1

at 9 GHz as a function of the applied magnetic field He W -- ^{- =} j ~ ' ( 0 ) 6 ( 0 - m(8)) d cos 0 (1) and a t room temperature. In figure 1 results are pre- YT

where

B2(0) = py(7c/2) (4 KM)' (3 cos2 0 - 1)"

FIG. 1. - The effective linewidth W as a function of the exter- nal magnetic field He at 9 GHz for polycrystalline YIG with porosities of 0.006, 0.015 and 0.04. Vertical lines indicate the

limits of the spin wave manifold. The dashed curve indicates the contribution from anisotropy broadening (calculated).

and

~ ( 0 ) = y { Hi(Hi i- 4 n M sin2 8) 1

.

In the expression (I) the factor B2(0) measures the strength of the coupling of the uniform precession (UP) to spin waves that propagate under an angle 8 with the z-axis. The delta function measures the density of states of the spin waves. In the limit Hi & 4 nM the integral of W over Hi, Nsw, equals p(2 n/5) (4 TcM)~, in good agreement with our experimental result for YIG. However, the expression (1) does not predict any relaxation outside the SW manifold. To improve the theory one must consider secondary scattering.

111.2. SECONDARY

: THE DENSITY OF

STATES.

- The perturbation by the pore mixes the

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971151

FERROMAGNETIC RELAXATION I N POROUS POLYCRISTALLINE FERRITES C 1 -157

spin waves and affects both the density of states of the nonuniform modes and the strength of their cou- pling to the UP. Motizuki. Sparks and Seiden (MSS) [3] replaced the delta function in (1) by a normalized distribution function

PI(^, 0, Hi) = (11~) wl(Hi, Hi<Q>) where

Hi(@ = - b + ^{{ (oly)'} + ^b2 1%

and

b = 2 n M s i n 2 0 .

The function w,(Hi, H(r)) describes the distribution of the z-component of the static internal field H(r) in the sample. This function has been considered by Schlomann 181 and Pointon et al. [9]. It is presented in figure 2 for p = 0.10. Although the function w,

FIG.

-The distribution functions wl and wn. The function

w l

is shown for a porosity 0.10. The function wz does not depend on porosity.

is non-zero over a field range 4 nM, it places the main emphasis on a much smaller range of the order of p. 4 nM around the unperturbed field value, corres- ponding to those parts of the sample that are not too close to the pore. The curve for W calculated according to the MSS theory for YIG with p = 0.04 is presented in figure 3. At the edges of the SW mani- fold Wfalls off to zero over a field range of the order of p.4 nM. (The MSS theory allows one to take into account a possible nonsphericity of the pores by a modification in BZ(0) which contains an adjustable parameter c. Sage [lo] has shown that c is restricted t o the values - 1 < c < 2. The curve of figure 3 has been calculated with

= 2). The modification introduced into the theory by MSS reflects the change in the density of states, but it overlooks the change in the coupling due to the secondary scattering.

111.3 SECONDARY SCATTERING : THE COUPLING. - Close to the pore the wave functions of the nonuni- form modes will be strongly perturbed. Since the coupling of these modes to the UP takes place through the demagnetizing fields which are concentrated around the pore, it will be modified considerably. Outside the SW manifold the nonuniform modes will be

({

local resonances D, which may be strongly coupled t o the UP and thus lead to large values of W, even

FIG. 3. - The effective linewidth W as a function of the exter- nal magnetic field He at 9 GHz for YIG with a porosity 0.04.

The experimental result (solid line) is compared to results calculated with the present theory (dashed line), and with a theory by Motizuki, Sparks and Seiden (dot-dashed line) in which the non-sphericity parameter c has been put equal to 2 (see text). Vertical lines indicate the limits of the spin-wave

manifold.

P-

though the density of states is small. It would be very complicated to calculate how the factor B2(0) should be modified. However, for anisotropy broa- dening [6, 71 we found that all effects of secondary scattering could be described fairly well by replacing the delta function in (I) by an effective distribution function, proportional to the effective linewidth W,, as calculated in the inhomogeneous broadening (IB) model. In that model [8] one has

Y l G POROSITY L %

-.-

We computed with the Kramers-Kronig rela- tions and obtained for WIB in the limit of very small P :

/."\ ----

/'

PRESENT THEORY

- -

0 3

where p = 3(Hi - w/y)/4 nM. The integral NIB of W,, over Hi is only 419 as large as Ns,, a result of the fact that dynamic demagnetizing fields are neglec- ted in the IB model. A similar situation was met in nuclear magnetic resonance (see e. g. Abragam [Ill).

The function w2(Hi, o/y) r W,,(Hi, u/y)/N,, is shown in figure 2. It gives much weight to the regions directly around the pore, where the field deviations are large, as required by our arguments about the coupling. We define the distribution function

which is normalized with respect to a. The curve for W calculated with the expression (1) in which 6(o - u(0)) is replaced by pz(o, 0, Hi) is shown in figure 3, together with the experimental results (YIG, p = 0.04) and the MSS result. Our theory describes very well the magnitude of W inside and above the manifold (i. e. for 2.4 kOe < He < 3.8 kOe). Below the manifold (3.8 kOe < He < 5 koe) the range over which the losses exist is calculated correctly, but the experimental values are a factor of two smal- ler than the calculated ones.

Acknowledgement. - The authors wish to thank

M. A. J. Breimer for performing the measurements.

C 1

-

^Q. H. F. VREHEN

BROESE

GROENOU

References

[I] VREHEN (Q. H. F.), J. Appl. Phys., 1969, 40, 1849. [7] VREHEN (Q. H. F.), BROESE

GROENOU (A.) and [2] SPARKS (M.), LOUDON (R.) and KITTEL (C.), Phys.

LAU (J. G . M.), Phys. Rev., B, 1970, B1,2332.

Rev., 1961, 122, 791. 181 SCHLOMANN (E.), Conf. Mag. Mag. Mat. AIEE [3] MOTIZUKI (K.), SPARKS (M.) and SEIDEN (P. E.), Spec. Pub., 1956, T-91, 600.

Phys. Rev., 1965, 140, A 972. [9] POINTON (A. J.) and ROBERTSON (J. M.), Phil. Mag., 141 SCHLOMANN (E.), Phys. Rev., 1969, 182, 632. 1965, 12, 725.

[5] PATTON (C. E.), Phys. Rev., 1969, 179, 352. [lo] SAGE (J. P.), Phys. Rev., 1969, 185, 859.

[6] VREHEN (Q. H. F.), BROESE

GROENOU (A.) and [ l l ] ABRAGAM (A.),

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DE

LAU (J. G. M.), Solid State Commun., 1969, tism,

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